# Sample partitioning estimation for ergodic diffusions: application to Ornstein-Uhlenbeck diffusion

Discussiones Mathematicae Probability and Statistics (2010)

- Volume: 30, Issue: 1, page 117-122
- ISSN: 1509-9423

## Access Full Article

top## Abstract

top## How to cite

topLuís Ramos. "Sample partitioning estimation for ergodic diffusions: application to Ornstein-Uhlenbeck diffusion." Discussiones Mathematicae Probability and Statistics 30.1 (2010): 117-122. <http://eudml.org/doc/277073>.

@article{LuísRamos2010,

abstract = {When a diffusion is ergodic its transition density converges to its invariant density, see Durrett (1998). This convergence enabled us to introduce a sample partitioning technique that gives in each sub-sample, maximum likelihood estimators. The averages of these being a natural choice as estimators. To compare our estimators with the optimal we obtained from martingale estimating functions, see Sørensen (1998), we used the Ornstein-Uhlenbeck process for which exact simulations can be carried out.},

author = {Luís Ramos},

journal = {Discussiones Mathematicae Probability and Statistics},

keywords = {ergodic diffusions; martingale estimating functions; transition and invariant densities; maximum likelihood estimators},

language = {eng},

number = {1},

pages = {117-122},

title = {Sample partitioning estimation for ergodic diffusions: application to Ornstein-Uhlenbeck diffusion},

url = {http://eudml.org/doc/277073},

volume = {30},

year = {2010},

}

TY - JOUR

AU - Luís Ramos

TI - Sample partitioning estimation for ergodic diffusions: application to Ornstein-Uhlenbeck diffusion

JO - Discussiones Mathematicae Probability and Statistics

PY - 2010

VL - 30

IS - 1

SP - 117

EP - 122

AB - When a diffusion is ergodic its transition density converges to its invariant density, see Durrett (1998). This convergence enabled us to introduce a sample partitioning technique that gives in each sub-sample, maximum likelihood estimators. The averages of these being a natural choice as estimators. To compare our estimators with the optimal we obtained from martingale estimating functions, see Sørensen (1998), we used the Ornstein-Uhlenbeck process for which exact simulations can be carried out.

LA - eng

KW - ergodic diffusions; martingale estimating functions; transition and invariant densities; maximum likelihood estimators

UR - http://eudml.org/doc/277073

ER -

## References

top- [1] B.M. Bibby and M. Sørensen, Martingale estimation functions for discretely observed diffusion processes, Bernoulli 1 (1995), 17-39. Zbl0830.62075
- [2] U. Küchler and M. Sørensen, Exponential Families of Stochastic Processes, Springer-Verlag 1997.
- [3] S. Iacus, Simulation and Inference for Stochastic Differential, Equations with R Examples, Springer 2008. Zbl1210.62112
- [4] J.T. Mexia and G.C. Dias, Statistical Inference for Discretely Observed Diffusions of Diffusions, VII-Congresso da SPE, 14-16 Outubro, Osir 1999.
- [5] B. Øksendal, Stochastic Differential Equations, An Introduction, Fifth Edition, Springer-Verlag 1998.
- [6] M. Sørensen, Lecture Notes on 'Statistical Inference for Discretely Observed Diffusions', Berlin Graduiertenkolleg 1998.